1. Field of the Invention
The present invention relates to a method of color correction and four-color conversion in an apparatus for recording a full-color image such as a color printer or a color duplicator.
2. Description of the Prior Art
The full-color recording on a hard copy is realized by gradation recording effected for each of a three-color ink including the three colors of cyan (C), magenta (M) and yellow (Y) or four-color ink including four colors with black (K) further added thereto. The gradation recording is roughly divided into a density gradation system typically including the thermal transfer system of sublimation type and the silver salt photography capable of controlling the density within a single dot, and a tone production system by density of each element such as the thermal transfer system of fusion type or the electrophotography for expressing a gradation with a combination of dots by using the integral effect of vision based on dither method or density pattern.
Either method uses the color reproduction on the principle of subtractive color mixture using complementary colors C, M, Y of the three primary colors of R, G, B. Compared with the color reproduction by additive color mixture the sole problem of which is the range of color reproduction by the three primary color but in which the spectral distribution of the color light has no effect on the color reproduction, the color reproduction by subtractive color mixture poses the problem of the spectral distribution of a dye having a great effect on the color reproduction.
In view of the fact that the spectral-absorption characteristic of actual ink has the central wavelength thereof displaced from an ideal form and the wavelength absorption characteristic thereof is so broad that there exists the phenomenon of subsidiary absorption, and the hue of the image recorded is changed to reduce the saturation.
To cope with these problems, the prior art uses a method called masking mainly in the field of printing.
The main densities c', m', y' for the central wavelength of the actual ink set by the linear masking are given by equations (1) below which represent a technique called linear masking and are widely used for their simple configuration. EQU c'=a0*c+al*m+a2*y EQU m'=a3*c+a4*m+a5*y EQU y'=a6*c+a7*m+a8*y (1)
The spectral densities c, m, y in equations (1) are those obtained when the inputs r, g, b are converted for complementary colors and are defined by equations (2) below. EQU c=log(1/r) EQU m=log(1/g) EQU y=log(1/b) (2)
The nine correction factors a0 to a8 in equations (1) are obtained first by determining a set of main densities (c', m', y') of actual ink for realizing colors in many sets of color patches (c, m, y) and then by minimizing the mean color difference therebetween.
The linear masking expressed by equations (1) implicitly assumes an addition theorem where the sum of density increase due to three amounts of dyes is equal to the increase in each density component, that is to say, the Lambert-Beer theorem concerning the densities in a subtractive color mixture.
In recording with actual ink superposition, however, it is known that such density linearity is not established, and in view of this, there has been proposed a high-order masking technique capable of expressing non-linearity to a certain degree.
Equations (3) represent the simplest secondary masking. EQU c'-a0*c+a1*m+a2*y+a3*c.sup.2 +a4*m.sup.2 +a5*y.sup.2 +a56*m*y+a7*y*c+a8*c*m EQU m'=a9*c+a10*m+a11*y+a12*c.sup.2 +a13*m.sup.2 +a14*y.sup.2 +a15*m*y+a16*y*c+a17*c*m EQU y'=a18*c+a19*m+a20*y+a21*c.sup.2 +a22*m.sup.2 +a23*y.sup.2 +a24*m*y+a25*y*c+a26*c*m (3)
As seen from this, the main density of the actual ink representing a particular color is expressed as a secondary equation of spectral densities c, m, y converted for complementary colors from input r, g, b, so that the non-linearity of density for superposed ink recording is approximated by a secondary equation. The 27 correction factors are determined to produce a minimum color difference in the average sense of the word against as many sets of color patches (c, m, y) as in the linear masking.
Also, tertiary or higher-order equations have been suggested to improve the approximation accuracy against the non-linearity of the superposed density.
The full-color reproduction on hard copy is realizable in principle by the three primary colors of C, M and Y. Actually, however, the gray scale by the combination of three colors C, M and Y is based on the balance therebetween. It is difficult to strike a perfect balance for all gradations, as the gray scale is often colored differently. Further, the density of black is often too low, or dignity of black is often insufficient with a color attached to the periphery of a pixel by displacement of the three-color pixels. In applications aimed at a high image quality, therefore, four-color recording, including black is used.
A conventional method to attain the four-color recording using black is called UCR (under color removal). In this method, the black ink density K is set to a given value less than amount of the ink lowest in density among Y, M and C; the black ink density thus set is subtracted from the density of each ink of Y, M and C.
Equations (4) represent an example of 100% UCR. Assuming that the ink densities of the three primary colors are C, M, Y and the density of black ink K, the value K is set to the minimum density among C, M and Y, the C, M, Y inks used for recording are expressed by C1, M1, Y1 respectively. EQU K=minimum (Y, M, C), C1=C-K EQU M1=M-K, EQU Y1=Y-K (4)
The conventional linear masking technique, in which the freedom is so limited that there are only nine correction factors to be optimized, facilitates optimization of the correction factors. Also, the comparatively small scale of hardware makes the conventional technique effective in an application not requiring a very faithful color reproduction. In view of fact that the non-linearity of density in the superposed color recording is corrected by linear operation, however, it is difficult to determine such a correction factor as to reduce the color difference over the entire color space, resulting in the problem of a great color difference with a target color.
The high-order masking technique, in which the approximating non-linearity of color reproduction reduces the color difference over the entire color space, is effective in attaining a faithful color reproduction. Since this method requires correction factors as many as 57 even for the third-order masking, many multipliers are required, thereby leading to a very large hardware scale. Even the simplest configuration of secondary order has 27 correction factors and is still very large in hardware scale.
Further, the high-order masking technique, with its high number of factors, has the problem that it is very difficult to determine an optimum correction factor by repeating recording tests or numerical calculations.
The problem of the conventional UCR (under color removal) technique for four-color reproduction, on the other hand, is that the four-color conversion with linear operation against the actual ink having a non-linear density in superposed color recording, rules out an accurate density forecast, with the result that the color obtained by superposing the four color inks is displaced from a target color.
As a consequence, a sufficiently faithful overall color reproduction cannot be attained simply by improving the masking accuracy in a high-order masking or the like, since the error due to UCR (under color removal) is considerable.